There's a popular "As Seen on TV" product called Slushy Magic that will turn any cold beverage into a slushy by shaking their "magic cubes" in the beverage for a few minutes. The cubes are just saltwater and they're forcing the same reaction that happens when making ice cream.

If you have a craving for ice cream but don't have any on hand you can make it yourself if you …
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Teaching weblog Charlie Brown's Teacher shares how all you need for your DIY version is a small durable freezer bag filled with saltwater. Mix salt and water together in a heavy-duty freezer bag, shake it until the salt is dissolved, and put the bag in the freezer overnight. Salt will lower the freezing temperature of the water so it will take longer to freeze but that also means it will be colder when used in your beverages.

Once this is complete, just put the frozen saltwater bag in a gallon-sized freezer bag with two cups of any sugar drink and shake it for a few minutes while the frozen saltwater freezes the drink into a slushy. The author notes that when she has tried to make a batch larger than two cups that she has reported saltwater leaking from the smaller freezer bag so look for a better container if you want to experiment with portion sizes.